SleepingInAirports.com recommends a big pair of headphones and a walkman to drown out the sound of airport announcements and to make the stay seem shorter. Of course, nowadays, everyone uses an iPod instead (and with the Griffin iTalk microphone, the iPod is a great fieldwork tool). I use it for all of my interviews as well as dictating notes to myself. They sync right back up to my laptop and I put them in the same folder as my written notes (now you can see why losing my laptop was such a big deal).
Rather than big "earmuff" headphones, I might also recommend inner-ear headphones such as the Sony MDR-EX71. I've had these now for about a month. These have silicon earplugs in various sizes that seal out outside sound much better than the open-air phones that come with the iPod. The sound quality is much better and it really quietens the roar of the airplane if you're sitting in the rear seats. I bought mine for just over Y4000 in Japan.
The one downside is that they seal out sound so well that you really have to be careful if you're walking around a busy city while wearing them. You can't hear bicycles or taxis that are bearing down on you with homicidal intent. You can also buy Shure high-end phones that look similar but cost over $200. I'm not that rich so I can't say if the sound is that much better.